A.G. MNUKHIN B.B. KOBYLANSKY Natioal Academy of Scieces of Ukraie Estimatig possible rate of ijuries i coal mies The article presets methods to calculate the values of ijury rates i mies. The authors demostrated how to estimate the value of compesatio paid to the ijured employees i the successive years (particularly ext year). The research was performed based o the data from several hard coal mies. key words: safety, occupatioal health ad safety, accidet rate, ijuries rate, predictig volume of compesatio paymets i the miig idustry.. INTRODUCTION Oe of the major ways to estimate risk i idustrial compaies with icreased degrees of hazards, particularly i coal mies, is to check the rate of the employees ijuries. The article features a aalysis of the rates of ijuries ad work-related diseases amog the employees of the coal idustry. I the article the authors used the data obtaied from the social ad accidet isurace compay of the Goriatska district i the tow of Makeevka, Makeevugol mie, Lei mie, Kholodaya Balka mie, Glubokaya mie, ad a private maufacturig compay Goriak-95. The Goriatska district is located i the souther part of Makeevka ad is the most populated district of the tow (populatio 99,800). I the paper the authors will determie the iitial dyamics of ijuries ad work-related diseases i Goriatska s coal mies. For this reaso, some data will be excluded from the obtaied data, i.e. the statistics of work-related diseases ad ijuries, alog with their dyamics, which are ot related to the operatios of the miig idustry. Additioally, the aalysis will ot cover the impact of demographic ad epidemic factors which icrease the rate of ijuries i the district. This way, excludig the ijuries ad diseases ot related to the miig idustry operatios, it is possible to correct the dyamics of the ijuries ad work-related diseases i miig compaies of the Goriatska district. Table features the results for the period 00-0, with the cosideratio of the ijuries rate for four mies. Ijuries rate 00-0 Table. Ijuries rate i coal mies 00 00 003 004 005 006 007 008 009 00 0 Lei mie 6 64 83 8 47 36 43 4 43 45 70 Kholodaya Balka mie 70 87 88 78 58 49 49 47 64 67 60 Goriak-95 7 4 3 3 0 8 0 5 4 7 6 Glubokaya mie 4 9 6 07 75 46 7 0 0 0 0 Based o the collected data, a chart was prepared to demostrate the chages i the ijuries rate i the give period (Fig. ). The aalytical form of the basic ijuries rate is usually expressed by a expoetial fuctio [, 4] ().
38 Miig Iformatics, Automatio ad Electrical Egieerig Fig.. Chages i the ijuries rate 00-0 t bt x ae () I the formula () x(t) stads for the basic value ijury rate i the momet t, startig from the first year of the previous decade; a, b are costat coefficiets; t time which passed from the first year of the previous decade. The coefficiets a ad b were determied accordig to the followig depedecies: ti lg xi ti i i b lgeti i i i ti lg xi i i i i ti ti i i lg xi, () ti ti lg xi lg a, (3) where x i the value of the ijuries rate i the year i; t i time which passed from the first year of the previous decade to the year i; п umber of observatios. The error of the predicted values of the ijuries rate is calculated accordig to the followig depedecy [3]: t j ti k m, (4) k where σ stadard deviatio; t i, t j time which passed from the first year of the previous decade respectively to the year i of the curret decade ad to the predicted year j; k i ti. (5) The value of the stadard deviatio is determied accordig to the followig depedecy [4,5]: zi zi (6) The predicted values of the ijuries rate are calculated accordig to the followig depedecy: x T bt ae m, (7) where Т time which passed from the first year of the previous decade to the predicted year. If the real values of the ijuries rate i the year for which the progosis was made are lower or equal to the values calculated accordig to the formula (4), it meas that the umber of ijuries remaied o the same level or decreased. If the real values are higher tha the calculatio values, that will idicate a real icrease i the umber of ijuries. The data from 00-00 (Table ) were used to calculate the coefficiets а ad b.
Nr 3(53) 05 39 Numerical data used to calculate the values a, b (Lei mie) Table. Data for calculatios Year N t i t i x i lgx i t i lgx i 00 6.785.785 00 4 64.806 3.6 003 3 3 9 83.99 5.757 004 4 4 6 8.908 7.634 005 5 5 5 47.67 8.360 006 6 6 36 36.556 9.338 007 7 7 49 43.633.434 008 8 8 64 4.63.986 009 9 9 8 43.633 4.70 00 0 0 00 45.653 6.53 Total 0 55 385 7.9 9.4 0 9,4 55 7,9 b 0,43430 385 55 0,067 ti k 5,5 5,5 3 5,5 4 5,5 5 5,5 6 5,5 7 5,5 8 5,5 9 5,5 0 5,5 85 385 7,9 55 9,4 lga,8797 0 385 55 a 76, For the coefficiet values calculated i this maer, the depedecy () takes the followig form: so 7,4 0 0 5,5 m,0, 0 85 x T 39 0,0. 0,067t00 t 76e x. Thus the predicted value of the total umber of people with ijuries i 0 will be equal to: 0,067*0 76 e 39 x, k 55 5,5 ; 0 Thus it is possible to draw a coclusio that, due to the real value of the total umber of ijuries i the mie beig 70 i 0 (i.e. twice as high as the computatioal oe), the performed calculatios give evidece of icreasig umber of ijuries i the Lei mie i 0. Similar calculatios were performed for the Kholodaya Balka mie. Numerical data used to calculate the values a, b (Kholodaya Balka mie) Table 3. Data for calculatios Year N t i t i x i lgx i t i lgx i 00 70.845.845 00 4 87.940 3.879 003 3 3 9 88.944 5.833 004 4 4 6 78.89 7.568 005 5 5 5 58.763 8.87 006 6 6 36 49.690 0.4 007 7 7 49 49.690.83 008 8 8 64 47.67 3.377 009 9 9 8 64.806 6.56 00 0 0 00 67.86 8.6 Total 0 55 385 8.069 97.809
40 Miig Iformatics, Automatio ad Electrical Egieerig 0 97,809 55 8,069 b 0,43430 385 55 0,0439 385 8,069 55 97,809 lga,98 0 385 55 a 8, thus the depedecy () has the followig form: k 0 55 5,5 ti k 5,5 5,5 3 5,5 4 5,5 5 5,5 6 5,5 7 5,5 8 5,5 9 5,5 0 5,5 85 0,78 0 0 5,5 m 3,0, 0 85 0,0439t00 t 8e x. The predicted value of the total umber of people with ijuries i 0 will be equal to: x 0,0439*0 8 e 53 The predicted value of the ijuries rate is: x T 53 3,0. The real value of the total umber of ijuries i the mie was 60 i 0. Due to the fact that the predicted value of the ijuries rate chages from 40 to 66, it ca be stated that the ijuries i the Kholodaya Balka mie remaied at the same level i 0. The data ad calculatios preseted below (Table 4) refer to the Goriak-95 compay. Numerical data used to calculate the values a, b (Goriak-95) Table 4. Data for calculatios Year N t i t i x i lgx i t i lgx i 00 7 0.845 0.845 00 4 4 0.60.04 003 3 3 9 3.36 4.085 004 4 4 6 3.4 4.456 005 5 5 5 0.000 5.000 006 6 6 36 8.55 7.53 007 7 7 49 0.000 7.000 008 8 8 64 5.76 9.409 009 9 9 8 4.46 0.35 00 0 0 00 7.30.304 Total 0 55 385 0.73 6.50 0 6,50 55 0,73 b 0,43430 385 55 0,0874 385 0,73 55 6,50 lga 0,8643 0 385 55 a 7, I this case the depedecy () takes the followig form 0,0874t00 t 7e x. The predicted value of the rate of total umber of people with ijuries i 0 will be equal to: x 0,0874*0 7 e 7 k 0 55 5,5 ti k 5,5 5,5 3 5,5 4 5,5 5 5,5 6 5,5 7 5,5 8 5,5 9 5,5 0 5,5 85 4,4 0 0 5,5 m 3,0, 0 85 x T 7 3,0. Whe aalyzig the obtaied results it ca be see that the real value of the rate of total ijuries umber i 0 was 6. As the predicted value of the ijuries rate chages from 4 to 0, it ca be stated that the ijuries rate for 0 icreased i Goriak-95.
Regressio aalysis impact of particular factors o the umber of ijuries ad the amouts of paid compesatio Table 5. Nr 3(53) 05 4
4 Miig Iformatics, Automatio ad Electrical Egieerig Coal output (y) depedig o the umber of employees (x ) ad the rate of ijuries (x ) a) y=.40x -8.4x -989.75 y.9x 3346.05 y.9x 3997.49 y.9x 694.6 Amout of compesatio paid to the ijured (y) depedig o the umber of people with ijuries (x) Kholodaya Balka b) y 85. x40.78. y x x 85. 40.78 8988.4 0.00065*( 6.5) 0.5 y 85.x 40.78 8988.4 0.00065* x 6.5 0. 5 Amout of compesatio paid to the ijured (y) depedig o the umber of people with ijuries (x) Goriak-95 c) y 85. x40.78 y x x 4.57 75.44 30.6 0.00065*( 5) 0.5 y x x 4.57 75.44 30.6 0.00065*( 5) 0.5 Amout of compesatio paid to the ijured (y) depedig o the umber of people with ijuries (x) Lei d) y 63.8 x 7490.64. y x x 63.8 7490.64 5863.9 0.00065*( 5.38) 0.5 y x x 63.8 75.44 5863.9 0.00065*( 5.38) 0.5 Aggregated data compesatio paid to the ijured (y) depedig o the umber of people with ijuries (x) (liear ad square fuctios) e) y67.78x933.49 ; y67.78x508.3, y 67.78x375. е) y 3.49x 390x 440.7 Fig.. Graphic illustratio of depedecies calculated i Table 5
Nr 3(53) 05 43 As it is possible to estimate the ijuries rate i the mies, it is desirable to pla compesatio paymets to the ijured people i the successive years (particularly ext year). The methods of parametric ad o-parametric statistics were used to determie ad aalyze a umber of depedecies. This way a comprehesive aalysis ca be performed to assess the process of idustrial accidets. I the further research the followig factors were take ito accout: daily output of coal (toes per day); umber of employees (people); umber of ijured employees (people); compesatio for the ijured (USD). The obtaied formulas ad the criteria of their statistical assessmet are demostrated i Table 5. As it ca be see, the majority are liear or square values. All preseted depedecies have, usually, sigificatly high values of correlatio coefficiets (twodimesioal or multi-dimesioal correlatio) ad determiatio coefficiets. I additio, they have a arrow rage of cofidece iterval values, determied at the sigificace level of 95%. Graphic iterpretatio of the obtaied formulas is preseted i Fig. a. Here it ca be observed that the Kholodaya Balka ijuries rate shows a costat tedecy to icrease alog with the icreasig coal output (higher itesity of works). The depedecies betwee compesatio paymets to the ijured ad the umber of people with ijuries i mies (Fig. b, c, d) ca be iterpreted as liear ad have a tedecy to decrease with the icreasig umber of the ijured, i.e. where the productio process is stable, the majority of ijuries are slight ad o-fatal ad their cosequeces are dealt with at low costs. The depedecy betwee compesatio paymets to the ijured (liked data) ad the umber of people with ijuries ca be iterpreted as liear (Fig. d) or o-liear (Fig. e), however, i this case it should be further ivestigated with the use of o-parametric statistics methods [,3,4]. The amout of compesatio paid to oe ijured perso i the successive years has a liear character ad a icreasig tedecy (Fig. 3 а, b, c for particular mies; Fig. 3 d aggregated data). It is also obvious (Fig. 3 a, b, c) that while i the Kholodaya ad Lei mies the cosequeces of ijuries are similar, the ew private compay Goriak achieved much better results, i.e. fewer ijuries ad, geerally, less serious oes. Goriak-95 а) y( x) 9.77 x 39554.9 b) y( x) 9.8x 9670.94 Lei Aggregated data c) y( x) 9.3x 3895.3 d) y( x) 8.9x 36407.86 Fig. 3 Amout of compesatio paid to oe ijured perso (y) i the successive years (x)
44 Miig Iformatics, Automatio ad Electrical Egieerig. CONCLUSIONS The coclusio we ca be draw from the above calculatios is that the level of ijuries icreases proportioally to the itesity of miig works. As a cosequece, the umber of compesatio paymets icreases too. It is iterestig to ote that the spedig o accidet isurace per oe employee (average real severity of ijuries) may be higher by more tha twice i oe mie tha i the other, though their miig ad geological coditios are very similar. Icreasig productio itesity requires to trai the persoel i the rage of safe workig methods ad to implemet ew, safer solutios [6]. The implemetatio of procedures that would improve the level of occupatioal health ad safety, alog with ew miig techologies, is likely to lower the spedig o compesatio paid to people ijured durig work-related accidets. The statistical models preseted i the article allow to estimate ad predict the level of ijuries ad, cosequetly, the amouts of compesatio paid to the ijured. I the further research it would be advisable to take ito accout the level of the employees awareess i the rage of occupatioal health ad safety, as well as the degree of progress i the applied miig techologies. Refereces. Kedall М., Stuart А.: Theory of Distributio. Мoscow: Nauka 966, p. 588.. Himmelblau D.: Aalysis of processes with the use of statistical methods. Moscow: Mir, 973, p. 959. 3. Hollader М., Wolfe D.: Nieparametrycze metody statystyki. Мoscow: Mir, 983, p. 58. 4. Mukhi А.G., Briuchaow А.М., Macho S.J., Kobylaskij B.B.: Predictig the ijuries rate i coal mies of Ukraie. Ugol Ukraiy Nr - 05, pp. 6-67. 5. Mosteller F.: Data aalysis ad regressio: i two editios. Editio / Traslatio from Eglish by J. N. Blagovieshtchasky; Ed:. J. P. Adler / Mosteller F., Tukey J. Moscow.: Fiasy i statistika, 98 p. 37. 6. Treczek S.: Kreowaie bezpieczego górictwa poprzez dostosowywaie przepisów i systemowego moitorowaia do zmieiających się waruków aturalych (Safe miig operatios through the adaptatio of regulatios ad system-based moitorig TO CHANGING NATURAL CONDITIONS). Mechaizacja i Automatyzacja Górictwa 03, str. 5-. The article was reviewed by two idepedet reviewers.